Automated workflow for 3d core digital modeling from computerized tomography scanner (cts) images

ABSTRACT

Computer-implemented methods, systems, and non-transitory computer-readable medium having computer program stored therein are provided to enhance the accuracy and efficiency of modeling a core sample from images of two-dimensional transverse sections of a core sample. Embodiments of the invention include, for example, image registering a plurality of images of transverse sections of a core sample to produce aligned transverse sections by approximating the circular location of the boundary of the transverse section and aligning the images based on center points of the approximated circles. Embodiments can further include, for example, performing a saw cut correction on the aligned transverse section images to adjust the images for the slab cut, generating a three-dimensional simulated model of the core sampling using or more of the saw cut line corrected images, and generating a three-dimensional simulated model of the internal composition of a borehole related to the core sample using multipoint statistics calculations.

RELATED APPLICATIONS

This application claims priority to and the benefit of U.S. ProvisionalPatent Application No. 61/909,212 titled “Automated Workflow for 3D CoreDigital Modeling From Computerized Tomography Scanner (CTS) Images”filed on Nov. 26, 2013, and is related to the non-provisional patentapplication filed on the same day as this application, Jun. 26, 2014,with the same above inventor and titled “Automated Saw Cut Correctionfor 3D Core Digital Modeling From Computerized Tomography Scanner (CTS)Images,” each of which is incorporated herein by reference in itsentirety.

BACKGROUND OF THE INVENTION

1. Field of Invention

Claimed embodiments of the invention relate to oil and gas reservoirmodeling and more particularly to computer-implemented methods, systems,and non-transitory computer-readable medium having one or more computerprograms stored therein to model a core sample or other rock sample.

2. Background of the Invention

A reservoir can be digitally modeled so as to reflect all of thereservoir's characteristics related to its ability to store and producehydrocarbons. Once completed, a reservoir model can be used to run flowsimulations to predict, for example, residual oil saturations orrecovery factors. These models, also called simulations, may be staticor dynamic. Static models are fine-scale reservoir models of rockproperties such as, for example, porosity, permeability, capillarypressure, fractures, faults, seismic attributes, and parameters that donot change significantly with time. Dynamic models, on the other hand,are coarser models. They incorporate fluid dynamic properties thatchange with time, such as, for example, pressure and flow rates ofhydrocarbons and water. Static models are sometimes calledreservoir-description grids or simply geological models, while dynamicmodels are sometimes called simulation grids.

Reservoir models may vary in scale from one another by as many as twelveorders of magnitude. For instance, one model might include pores, whichcan be measured in nanometers, while another model might represent afull oil field, which can be measured in kilometers. Highly-detailedmodels are often unsuitable for simulations. Consequently, detailedmodels are sometimes “scaled up” or “coarsened;” this process isreferred to as “upscaling.” Upscaling is accomplished through the use ofvarious algorithms. After upscaling has occurred, detailed features areno longer represented, but broader characteristics are still representedin the model.

Reservoir models can be developed in a variety of ways and from avariety of data sources. For example, some models are developed fromborehole images. Borehole images can be acquired through severaltechniques. One such technique is to use electrode pads placed againstthe wellbore wall around the wellbore to force a current through therock; sensors can then measure the current and map resistivities of thematerial surrounding the wellbore. The readings can then be used todevelop an image of the material and features, e.g., vugs, that make upthe sampled portions of the wellbore wall. Statistical techniques suchas multipoint statistics (MPS) can be used to model the full wellborewall, including gaps between the sampled images. MPS employs “trainingimages” as templates in modeling reservoir properties. Training imagescan be existing geological interpretations, but they do not need to be.

Another method of modeling a reservoir is the numerical pseudocoresmethod. In that method, numerical pseudocores are three-dimensionalmodels derived from both borehole images and digital rock samples. Themethod utilizes MPS, and the digital rock samples serve as trainingimages.

Digital rock samples—digital representations of core samples or otherrock samples—can be constructed from image sets obtained by, forexample, x-ray computed tomography (CT) scan (CTS), micro-CT scan, orconfocal microscopy. To obtain image sets by CTS, an x-ray is passedthrough two-dimensional transverse sections of a core sample from allsides of the sample, and density is calculated. Micro-CT scan similarlyuses x-ray technology to obtain images. Confocal microscopy usesfluorescence properties of different materials to create images. After“scanning” a number of transverse sections of the core sample, athree-dimensional model of the sample can be constructed. The model willshow the rock and its features, e.g., vugs.

To construct a model of a core sample, the scanned images of transversesections of the core sample must often be manipulated. The process ofmanipulating the images, however, frequently requires subjectivedecision-making and variable adjustments by individuals. These factorscause the process of constructing a model to be time-consuming andresult in models that are often prone to inaccuracies.

SUMMARY OF THE INVENTION

Applicant has recognized problems associated with the process ofmodeling a core sample and has advantageously developedcomputer-implemented methods, systems, and one or more non-transitorycomputer-readable mediums having one or more computer programs storedtherein to enhance the accuracy and efficiency of modeling a coresample. Embodiments of the invention relate to image manipulation todevelop models of a core sample or other rock sample that can be used,for example, to generate numerical pseudocores. Rather than relying onsubjective decision-making and variable adjustments by individuals,embodiments of the invention include, for example, elegant automatedtechniques that enhance the image manipulation and modeling process byreducing inaccuracies and increasing time efficiency.

Embodiments of the invention include computer-implemented methods ofprocessing two-dimensional images of two-dimensional transverse sectionsof a real, three-dimensional, substantially cylindrical core sample ofsubsurface material so as to be able to simulate a three-dimensionalmodel of the core sample. Methods can include image registering theimages to align the images along an appropriate axis for modeling,removing surface artifact by cropping portions of the images that resultfrom noise, and generating a model of the core sample from the images.To image register the images, methods can include approximating circularlocation of peripheries of the representation of a transverse section inan image to produce an approximated circular boundary. Peripheries ofthe representation are a boundary between a representation of atransverse section in an image and a background that substantiallysurrounds the representation. Methods can also include selecting acenter point of the approximated circle in each image to serve as areference point for each representation of a transverse section,determining a simulated axis that is an imaginary line that passesthrough the reference point of the representation of one transversesection and extends substantially perpendicularly to the plane of thatrepresentation of a transverse section, and aligning each referencepoint on the simulated axis, with each representation of the transversesections arranged in sequential order. To remove surface artifact,methods can include cropping a portion of each of the aligned transversesections such that they form simulated peripheries to be substantiallysimilar in size, thereby producing a plurality of cropped alignedtransverse sections that include the aligned transverse sections andexclude the cropped portions. Methods can also include generating asimulated model of the core sample that includes the cropped alignedtransverse sections in their sequential order. The model can bethree-dimensional, and it can depict the internal composition of thestructural characteristics of the core sample, including vugs and poreswithin the material, for example. Methods can further includeapproximating circular location of the boundary for each image bydetermining a perpendicular bisector of each side of the images,selecting four or more points on the representation that intersects withthe perpendicular bisectors, selecting at least three out of the four ormore points to form an imaginary triangle for each of the four or morepoints, determining a circumcenter of each of the imaginary triangles,and determining a radius of a plurality of imaginary circles, the centerof each of the imaginary circles being one of circumcenters of theimaginary triangles. Method embodiments can further include, forexample, comparing each radius of the plurality of imaginary circles toa predetermined radius of the core sample, and selecting the circlehaving the smallest difference between its radius and the predeterminedradius of the core sample as the approximated circular boundary.

Embodiments of the invention further include computer-implementedmethods of performing a saw-cut correction when, for example, the imagesare digital images having a plurality of pixels and the core sample hasa slab cut (e.g., a portion of the sample removed when the sample wascut from the borehole). Methods can include, for each aligned image,discarding the background of the aligned image, identifying two or morepixels in the aligned image that have a value of zero, and determiningan imaginary best-fit line for the pixels that have a value of zero tothereby identify a saw cut line. Methods can include approximatingcircular location of peripheries of the aligned transverse section in analigned image to thereby identify an approximated slab cut boundary toapproximate the position of a boundary between the aligned transversesection and a background substantially surrounding the alignedtransverse section in the aligned image. Embodiments of the inventioncan further include, for example, comparing a number of non-zero pixelson a first side of the saw cut line with a number of non-zero pixels ona second side of the saw cut line. The portion of the representationwith the smaller number of non-zero pixels relative to the saw cut linebeing the smaller portion of the representation and the larger portionbeing the portion of the representation associated with the largernumber of non-zero pixels. Methods can further include, for example,identifying a point positioned on peripheries of the smaller portion tothereby identify a standalone point, determining an imaginary lineperpendicular to the saw cut line that extends through the standalonepoint to thereby identify a reference line, and moving the smallerportion parallel to the reference line to position the standalone pointon peripheries of the approximated circular boundary.

Embodiments of the invention also include systems to processtwo-dimensional images of two-dimensional transverse sections of a real,three-dimensional, substantially cylindrical core sample of subsurfacematerial so as to be able to simulate a three-dimensional model of thecore sample. Systems can include one or more processors, an input andoutput unit in communication with the one or more processors, one ormore displays in communication with the one or more processors, and oneor more non-transitory memories in communication with the one or moreprocessors. The one or more non-transitory memories can includecomputer-readable instructions such as a computer program that whenexecuted cause the system to perform a series of steps to manipulateimages. The steps can include image registering the images to align theimages along an appropriate axis for modeling, removing surface artifactby cropping portions of the images that result from noise, andgenerating a model of the core sample from the images. To image registerthe images, the steps can include approximating circular location ofperipheries of the representation of a transverse section in an image toproduce an approximated circle. The steps can also include selecting acenter point of the approximated circle in each image to serve as areference point for each representation of a transverse section,determining a simulated axis that is an imaginary line that passesthrough the reference point of the representation of one transversesection and extends substantially perpendicularly to the plane of thatrepresentation of a transverse section, and aligning each referencepoint on the simulated axis, with each representation of the transversesections arranged in sequential order. To remove surface artifact, thesteps can include cropping a portion of each of the aligned transversesections such that they form simulated peripheries to be substantiallysimilar in size, thereby producing a plurality of cropped alignedtransverse sections that include the aligned transverse sections andexclude the cropped portions. The steps can also include generating asimulated model of the core sample that includes the cropped alignedtransverse sections in their sequential order. The model can bethree-dimensional, and it can depict the internal composition of thestructural characteristics of the core sample, including vugs and poreswithin the material, for example.

The steps can further include approximating circular location of theboundary for each image by determining a perpendicular bisector of eachside of the images, selecting four or more points on the representationthat intersects with the perpendicular bisectors, selecting at leastthree out of the four or more points to form an imaginary triangle foreach of the four or more points, determining a circumcenter of each ofthe imaginary triangles, and determining a radius of a plurality ofimaginary circles, the center of each of the imaginary circles being oneof circumcenters of the imaginary triangles. The steps can furtherinclude, for example, comparing each radius of the plurality ofimaginary circles to a predetermined radius of the core sample, andselecting the circle having the smallest difference between its radiusand the predetermined radius of the core sample as the approximatedcircular boundary.

The steps can also include performing a saw-cut correction when, forexample, the images are digital images having a plurality of pixels andthe core sample has a slab cut and is a slab cut core sample. The stepscan include, for each aligned image, discarding the background of thealigned image, identifying two or more pixels in the aligned image thathave a value of zero, and determining an imaginary best-fit line for thepixels that have a value of zero to thereby identify a saw cut line. Thesteps can include approximating circular location of peripheries of thealigned transverse section in an aligned image to thereby identify anapproximated slab cut circular boundary. The steps can further include,for example, comparing a number of non-zero pixels on a first side ofthe saw cut line with a number of non-zero pixels on a second side ofthe saw cut line. The portion of the representation with the smallernumber of non-zero pixels relative to the saw cut line being the smallerportion of the representation and the larger portion being the portionof the representation associated with the larger number of non-zeropixels. The steps can further include, for example, identifying a pointpositioned on peripheries of the smaller portion to thereby identify astandalone point, determining an imaginary line perpendicular to the sawcut line that extends through the standalone point to thereby identify areference line, and moving the smaller portion parallel to the referenceline to position the standalone point on peripheries of the approximatedcircular boundary.

A system according to embodiments of the invention can also include acore sample imaging device that can capture images of transversesections of a core sample, such as, for example, a computerizedtomography scanner. The steps can then further include capturing aplurality of images before image registering the images.

Embodiments of the invention include non-transitory computer-readablemedium, such as computer memories, that has computer program storedtherein that when executed causes a computer to take steps to processtwo-dimensional images of two-dimensional transverse sections of a real,three-dimensional, substantially cylindrical core sample so as to beable to simulate a three-dimensional model of the core sample. The stepscan include image registering the images to align the images along anappropriate axis for modeling, removing surface artifact by croppingportions of the images that result from noise, and generating a model ofthe core sample from the images. To image register the images, the stepscan include approximating circular location of peripheries of therepresentation of a transverse section in an image to produce anapproximated circle. Peripheries of the representation are a boundarybetween a representation of a transverse section in an image and abackground that substantially surrounds the representation. The stepscan also include selecting a center point of the approximated circle ineach image to serve as a reference point for each representation of atransverse section, determining a simulated axis that is an imaginaryline that passes through the reference point of the representation ofone transverse section perpendicularly to the plane of thatrepresentation of a transverse section, and aligning each referencepoint on the simulated axis, with each representation of the transversesections arranged in sequential order. To remove surface artifact, thesteps can include cropping a portion of each of the aligned transversesections such that they form simulated peripheries to be substantiallysimilar in size, thereby producing a plurality of cropped alignedtransverse sections that include the aligned transverse sections andexclude the cropped portions. The steps can also include generating asimulated model of the core sample that includes the cropped alignedtransverse sections in their sequential order. The model can bethree-dimensional, and it can depict the internal composition of thestructural characteristics of the core sample, including vugs and poreswithin the material, for example.

The steps can further include approximating circular location of theboundary to thereby identify an approximated circle for each image bydetermining a perpendicular bisector of each side of the images,selecting four or more points on the representation that intersects withthe perpendicular bisectors, selecting at least three out of the four ormore points to form an imaginary triangle for each of the four or morepoints, determining a circumcenter of each of the imaginary triangles,and determining a radius of a plurality of imaginary circles, the centerof each of the imaginary circles being one of circumcenters of theimaginary triangles. Method embodiments can further include, forexample, comparing each radius of the plurality of imaginary circles toa predetermined radius of the core sample, and selecting the circlehaving the smallest difference between its radius and the predeterminedradius of the core sample as the approximated circular boundary.

Embodiments of the invention further include non-transitorycomputer-readable medium having computer program stored therein thatwhen executed causes a computer to further take steps to perform asaw-cut correction when, for example, the images are digital imageshaving a plurality of pixels and the core sample has a slab cut. Thesteps can include, for each aligned image, discarding the background ofthe aligned image, identifying two or more pixels in the aligned imagethat have a value of zero, and determining an imaginary best-fit linefor the pixels that have a value of zero to thereby identify a saw cut.The steps can include approximating circular location of peripheries ofthe aligned transverse section in an aligned image to thereby identifyan approximated slab cut circle to approximate the position of aboundary between the aligned transverse section and a backgroundsubstantially surrounding the aligned transverse section in the alignedimage, identifying a portion of an aligned transverse section positionedto have the boundary of the aligned transverse section the portionsubstantially within a region that is enclosed by the approximated slabcut circle and the saw cut to thereby identify a detached portion, andidentifying a point positioned on the detached portion and on theboundary between the representation of the aligned transverse sectionand the background that substantially surrounds it to thereby identify astandalone point. The steps can further include determining an imaginaryline that is perpendicular to the saw cut and passes through thestandalone point to thereby identify a reference line and moving thedetached portion parallel to the reference line and away from the sawcut such that the standalone point is positioned on the approximatedslab cut circle.

BRIEF DESCRIPTION OF THE DRAWINGS

The application file contains at least one drawing executed in color.Copies of this patent application publication with color drawings willbe provided by the Patent and Trademark Office upon request and paymentof the necessary fee.

FIG. 1 is a schematic diagram of a system to manipulate images oftwo-dimensional transverse sections of a core sample according to anembodiment of the invention.

FIG. 2 is a schematic method flow diagram of a method to process imagesof two-dimensional transverse sections of a core sample according to anembodiment of the invention.

FIG. 3 is a schematic diagram of a core sample according to anembodiment of the invention.

FIG. 4 is a schematic diagram of a core sample model according to anembodiment of the invention.

FIG. 5 is a schematic diagram of an image of a transverse section of acore sample according to an embodiment of the invention.

FIG. 6 is a set of schematic diagrams of core samples according to anembodiment of the invention.

FIG. 7 is a schematic diagram of a core sample according to anembodiment of the invention.

FIG. 8 is a schematic diagram of a model of an askew core sample modelaccording to an embodiment of the invention.

FIG. 9 is a schematic diagram of a set of images of transverse sectionsof an askew core sample according to an embodiment of the invention.

FIG. 10 is a schematic diagram of a model of an askew core sample modelaccording to an embodiment of the invention.

FIG. 11 is a schematic diagram of aligned images of a transverse sectionof a core sample according to an embodiment of the invention.

FIG. 12 is a schematic diagram of an image of a transverse section of acore sample according to an embodiment of the invention.

FIG. 13 is a schematic diagram of an image of a transverse section of acore sample according to an embodiment of the invention.

FIGS. 14A-D each illustrates a schematic diagram of an image of atransverse section of a core sample according to an embodiment of theinvention.

FIG. 15 is a schematic diagram of an image of a transverse section of acore sample according to an embodiment of the invention.

FIG. 16 is a schematic diagram of an image of a transverse section of acore sample according to an embodiment of the invention.

FIG. 17 is a schematic diagram of an image of a transverse section of acore sample according to an embodiment of the invention.

FIG. 18 is a schematic diagram of a set of aligned images of transversesections of a core sample according to an embodiment of the invention.

FIG. 19 is a schematic diagram of a core sample model according to anembodiment of the invention.

FIG. 20 is a schematic diagram of an image of a transverse section of acore sample according to an embodiment of the invention.

FIG. 21 is a plurality of schematic diagrams of images of transversesections according to an embodiment of the invention.

FIG. 22 is a schematic diagram of an image of a transverse section of acore sample according to an embodiment of the invention.

FIG. 23 is a schematic diagram of an approximated slab cut boundary of atransverse section of a core sample according to an embodiment of theinvention.

FIG. 24 is a schematic diagram of an image of a transverse section of acore sample according to an embodiment of the invention.

FIG. 25 is a schematic diagram of a core sample according to anembodiment of the invention.

FIG. 26 is a schematic diagram of a system to manipulate images oftwo-dimensional transverse sections of a core sample according to anembodiment of the invention.

FIG. 27A is a schematic diagram of a model of a borehole according to anembodiment of the invention.

FIG. 27B is a schematic diagram of a model of a borehole according to anembodiment of the invention.

FIG. 28 is a schematic diagram of an image of transverse sections of acore sample according to an embodiment of the invention.

FIG. 29 is a schematic diagram of an image of transverse sections of acore sample according to an embodiment of the invention.

FIG. 30 is a schematic diagram of an image of transverse sections of acore sample according to an embodiment of the invention.

FIG. 31 is a schematic diagram of an image and saw cut line of atransverse section of a core sample according to an embodiment of theinvention.

FIG. 32 is a schematic diagram of an image of a transverse section of acore sample according to an embodiment of the invention.

FIG. 33 is a schematic diagram of an image of a transverse section of acore sample according to an embodiment of the invention.

FIG. 34 is a schematic diagram of a computer program to process imagesof two-dimensional transverse sections of a core sample according to anembodiment of the invention.

FIG. 35 is a schematic method flow diagram of a method to process imagesof two-dimensional transverse sections of a core sample according to anembodiment of the invention.

FIG. 36 is a schematic method flow diagram of a method to image registerimages of two-dimensional transverse sections of a core sample accordingto an embodiment of the invention.

FIG. 37 is a schematic method flow diagram of a method to approximatecircular location of a boundary of an image according to an embodimentof the invention.

FIG. 38 is a schematic method flow diagram of a method to determineimaginary circles according to an embodiment of the invention.

FIG. 39 is a schematic method flow diagram of a method to process imagesof two-dimensional transverse sections of a core sample according to anembodiment of the invention.

FIG. 40 is a schematic method flow diagram of a method to perform a sawcut correction according to an embodiment of the invention.

FIG. 41 is a schematic method flow diagram of a method to perform a sawcut correction according to an embodiment of the invention.

FIG. 42 is a schematic method flow diagram of a method to approximatecircular location of a slab cut boundary for an image according to anembodiment of the invention.

FIG. 43 is a schematic method flow diagram of a method to determineimaginary circles according to an embodiment of the invention.

FIG. 44 is a schematic diagram of an imaginary triangle according to anembodiment of the invention.

DETAILED DESCRIPTION OF THE INVENTION

So that the manner in which the features and advantages of theembodiments of methods, systems, and non-transitory computer-readablemedium having computer program stored therein of the present invention,as well as others, which will become apparent, may be understood in moredetail, a more particular description of the embodiments of methods,systems, and non-transitory computer-readable medium having computerprogram stored therein of the present invention briefly summarized abovemay be had by reference to the embodiments thereof, which areillustrated in the appended drawings, which form a part of thisspecification. It is to be noted, however, that the drawings illustrateonly various embodiments of the embodiments of methods, systems, andnon-transitory computer-readable medium having computer program storedtherein of the present invention and are therefore not to be consideredlimiting of the embodiments of methods, systems, and non-transitorycomputer-readable medium having computer program stored therein of thepresent invention's scope as it may include other effective embodimentsas well.

Embodiments of the invention provide, for example, image manipulation todevelop models of a core sample (or other rock sample) to generatenumerical pseudocores. Rather than relying on subjective decision makingor variable adjustments by individuals, embodiments of the inventionprovide, for example, automated techniques that enhance the imagemanipulation and modeling processes by reducing inaccuracies andincrease time efficiency. More specifically, embodiments of theinvention include, for example, systems, non-transitory memories havingone or more computer programs stored therein, and computer-implementedmethods of processing a plurality of two-dimensional images of a coresample to simulate a three-dimensional model of the core sample.

To simulate a three-dimensional model of a real, three-dimensional,substantially cylindrical core sample, a plurality of two-dimensionalimages of transverse sections of the core sample are processed ormanipulated. For example, images of transverse sections of the coresample can be acquired by a computerized tomography (CT) scanner orother image device as illustrated in FIG. 1, for example. After the CTimages are acquired 50, the images can undergo an image registrationprocess 51 as illustrated in FIG. 2. Next, the images can undergo a sawcut correction 52, followed by an artifact removal 53, and a beamhardening correction 54. The results can be a core sample model 300, asillustrated in FIG. 4, for example, which can be used as a trainingimage for multi-point statistics modeling 55 to produce a borehole model500.

An overview of generating a three-dimensional simulated model of aborehole model 500, according to computer-implemented method embodimentof the invention, can be described briefly with reference to FIG. 35. Acomputer-implemented method embodiment can include for example,capturing in step 600, a plurality of two-dimensional images of aplurality of transverse sections of a real core sample using an imagingdevice, and image registering in step 601, the images to produce alignedtransverse sections. After images are aligned, a computer-implementedmethod embodiment can further include, for example, performing a saw cutcorrection in step 602 on the aligned transverse sectional images. Asunderstood by those skilled in the art, a core sample is sometimes cutwith a saw or other cutting tool to facilitate removing the sample fromthe borehole. This causes the core sample to have two pieces that areoften put together during images. However, this is not the originalshape of the core sample and is therefore sometimes an undesirableprocessing artifact for three-dimensional modeling. Accordingly,embodiments of the invention include a saw-cut correction process 52 sothat the images more accurately reflect the original shape of the coresample.

After saw-cut correction, a computer-implemented method embodimentincludes, for example, cropping in step 603, a portion of each of thealigned transverse sections to remove core surface artifacts to producecropped aligned transverse sections. Computer-implemented methodembodiments can also include, for example, performing a polynominalregression in step 604, on computerized tomography data points tocorrect for beam hardening phenomena, as understood by those skilled inthe art. Computer-implemented method embodiments can also include, forexample, generating in step 605, a three-dimensional simulated model ofthe internal composition of the structural characteristics of the coresample using the cropped aligned transverse sections. The model 300 candepict the internal composition of the structural characteristics of thecore sample 100, including vugs and pores within the material, forexample. Embodiments can also include generating in step 606, athree-dimensional simulated model 500 of the internal composition of thestructural characteristics of a borehole related to the core sample 100to illustrate the borehole's interior structure and material as shown,for example, in FIGS. 27A and 27B, by using multi-point statisticstechniques, utilizing a model 300 of a core sample 100 as a trainingimage.

FIG. 1 illustrates a system for processing a plurality oftwo-dimensional images 150 of a core sample 100 of subsurface materialaccording to an embodiment of the invention. A computerized tomography(CT) scanner, micro-CT scan, confocal microscopy, or other imagingdevice can be used to acquire images 150 of the core sample 100. X-rays32 from an x-ray source 30 pass through a collimator 31 and permeate thecore sample 100 as the core sample 100 rotates 34. A detector array 33measures the intensity of the x-rays 32 on the other side of the coresample 100 from the x-ray source 30. This produces, for example, animage 150 of a transverse section 110 of the core sample 100. Thisprocess is repeated to acquire a plurality of transverse sectionalimages 150 each comprised of a plurality of pixels. Each image 150, asillustrated in FIGS. 3 and 5, is polygon shaped and comprises asubstantially annular representation 151 of a different transversesection 110 of the core sample and a background 152 that substantiallysurrounds the representation 151. One or more of the transverse sections110 can be closer to a first 102 or second 103 end of the core sample,or positioned there between, as illustrated in FIG. 6 for example.According to some embodiments, the plurality of transverse sections 110have a sequential order based on their individual positions within thecore sample 100 from the first end 102 to the second end 103, or viceversa. The radius 101 or the diameter of the core sample can be measuredto facilitate modeling. According to certain embodiments, the radius 101of the core sample that can be determined by measuring the distance fromthe edges of the core sample 100 to an imaginary axis 104 of the coresample 100 that extends substantially through a medial portion of thecore sample 100, as shown in FIG. 7, for example. The imaginary axis 104can be determined by connecting the centers of the first end 102 and thesecond end 103 of the core sample 100.

After the pluralities of images are captured, embodiments of the presentinvention can include an image registering process 51 to align theplurality of images. Assembling each image 150 on top of one anotherwithout correcting the position of the representation 151 of thetransverse section 110 in the image 150 can produce an askew core samplemodel 62, as illustrated in FIG. 8. Uncorrected images 60, asillustrated in FIG. 9, include an approximate location 61 of arepresentation 151, and when the uncorrected images 60 are assembled ontop of one another, they can produce an inaccurate askew core samplemodel. To mitigate or prevent this skewing effect, embodiments of theinvention include automated image registering 51 the images to producealigned transverse sectional images.

General aspects of image registering images to produce alignedtransverse sections, according an embodiment of the invention, can bedescribed briefly with reference to FIG. 36. Embodiments of imageregistration can include, for example, approximating in step 610, thesubstantially circular boundary for each representation 151 of atransverse section 110, selecting in step 611, a center reference pointof each of the approximated boundaries 611, determining in step 612, asimulated axis that passes through each reference point 612 to produce asimulated axis, and aligning in step 613, each of the reference pointson the simulated axis to produce aligned transverse sections of the coresample. More particular aspects of image registering a plurality ofimages to produce aligned transverse sections, according to variousembodiments, are described further herein. After the images are aligned,embodiments can further include, for example, cropping in step 603, aportion of each of the aligned transverse sections to remove coresurface artifacts, and generating in step 605, a three-dimensionalsimulated model of the internal composition of the structuralcharacteristics of the core sample. Each of the foregoing are describedin more detailed below.

To align the plurality of images 150, embodiments of the invention caninclude systems, non-transitory memories having one or more computerprograms stored therein, and computer-implemented methods ofapproximating the substantially circular boundary 153 of therepresentation 151 (e.g., the outer peripheries of the depiction of thetransverse section of the core sample). Approximating the circularboundary 153 according to various embodiments can be described brieflywith reference to FIG. 37. Embodiments of approximating thesubstantially circular boundary can include, for example, the steps ofdetermining in step 620, the perpendicular bisectors of each side of theimage 150, and determining in step 621, four points on therepresentation 151 that intersect with the perpendicular bisectors.Embodiments of the invention can further include, for example,determining in step 622, an imaginary circle for each of the four pointson the representation, calculating in step 623, the radius of each ofthe imaginary circles, comparing in step 624, each radius of theimaginary circles to a predetermined radius of the core sample, andselecting in step 625, the imaginary circle with the smallest differencebetween its radius and the predetermined radius. According to variousembodiments of the invention, the approximated circular boundary 212 isthe imaginary circle having the smallest difference between its radiusand the predetermined radius of the core sample.

FIG. 12 illustrates the perpendicular bisectors 220 of a polygon shapedimage 150 and four points 205 on the representation 151 that intersectwith the perpendicular bisectors 220 (see e.g., line 221, whichinterests with points 220 and 205). The perpendicular bisectors 220 ofthe image, for example, can be determined by calculating the number ofpixels per direction and dividing this number by half for each side ofthe image. Points 205 on the representation 151 are automaticallydetermined, according to various embodiments, by locating, for example,one or more first non-zero pixels when moving from an initial positionof a side of the image towards the center of the representation. Pixelsthat are substantially black have values that are at or near zero.Accordingly, identifying one or more first non-zero pixels (e.g., colorpixels) for each side of the image will identify one or more points 205on the boundary 153 of the representation 151 of the core sampleaccording to an embodiment of the invention. To facilitate identifyingthe points 220 on the representation 151, certain embodiments include,discarding the background 152 before identifying the points 220 on therepresentation 151 so that the area between the sides of the image andthe representation 151 is substantially void of color pixels, including,for example, dark blue.

In some embodiments, four or more points 205 on the representation 151are selected. In other embodiments, less than four points 205 on therepresentation 151 are selected. In some embodiments of the invention,the points 220 on the boundary 153 of the representation 151 aredetermined by locating one or more first non-zero pixels. According toan exemplary embodiment, the selected points 205 on the representation151 are perpendicular to the perpendicular bisectors 220 of the image150 as illustrated in FIG. 12 for example. According to certainembodiments, the selected points 205 on the representation are notperpendicular to the perpendicular bisector 220 of the image 150 but areidentified as being one or more first non-zero pixel and therefore onthe periphery 153 of the representation 151.

After the points 205 on the periphery 153 of the representation 151 areselected, embodiments of the invention can further include determiningan imaginary circle 211 for each of the points 205 on therepresentation. Aspects of determining the imaginary circles 211,according to an embodiment of the invention, can be described brieflywith reference to FIG. 38, for example. Embodiments of determining orforming an imaginary circle 211 for each of the four points 205 on therepresentation 151 can include, for example, selecting in step 614 ofFIG. 38, three of the four points to form an imaginary triangle 800, asillustrated in FIG. 47. An imaginary triangle 800 is formed, forexample, for each mathematical combination of three of the four selectedpoints 205. Embodiments can further include, for example, determining instep 615, the circumcenter 801 of the imaginary triangle 800, anddetermining in step 616 an imaginary circle 211 for each of the fourpoints 205, where the center of each of the imaginary circles is thecircumcenter 801 of the imaginary triangle 800, as illustrated in FIG.47. According to other embodiments, more or less points 205 on therepresentations are selected to determine the imaginary circles 211.According to certain embodiments, to determine the imaginary circles211, the mathematical combinations of a subset of the selected points205 on the representation are selected such that the peripheries of theimaginary circle 211 interconnects the subset of the selected points.

FIG. 13 illustrates an imaginary circle 211 for each of the four points205 on the periphery 153 of the representation 151 according to anembodiment of the invention. In this example embodiment, each circle 211interconnects three of the four points 205 on the representation. Afterthe imaginary circles 211 are determined, embodiments of the inventioncan include determining the radius of each circle 211 (see e.g., thelines connected to the center 210 of each imaginary circle 211 in FIG.13) and selecting the circle 212 with the smallest difference from apredetermined radius of the core sample as the approximate boundary 180.FIGS. 14A-D each illustrates, for example, one of the plurality ofimaginary circles 211. In this example embodiment, the circle 212illustrated in FIG. 14B is the approximated boundary because it has thesmallest difference from a predetermined radius of the core sample. FIG.16 illustrates, for example, the approximated boundary 180 of therepresentation 151 according to an embodiment of the invention, and theboundary 153 of the representation as depicted from imaging. Embodimentsof using imaginary circles 211 to approximate the boundary 180 of arepresentation 151 can be used for images of a whole core 130, images ofa core sample with a slab cut 131, and images of a partial core 132, asillustrated in FIG. 21. FIG. 15, for example, illustrates a plurality ofimaginary circles 211 for a partial core sample or a core sample with aslab cut and is discussed further below.

Referring back to FIG. 36, approximating in step 610, the substantiallycircular boundary 180 is performed for each of the plurality of imagesof the core sample as part of various embodiments of image registeringimages to produce aligned transverse sections. Embodiments of imageregistration can further include, for example, selecting in step 610 acenter point 185 of each of the approximated circular boundaries 180 toserve as a reference point 185, as illustrated in FIG. 16, anddetermining in step 612 an imaginary line that passes through thereference point 185 of the representation 151 of the first endtransverse section and extends substantially perpendicularly to theplane of the representation of the first end transverse section tothereby identify a simulated axis 186, as illustrated in FIG. 17.Embodiments can also include aligning in step 613, each reference point185 of the images 190 on the simulated axis 186, with eachrepresentation 151, as illustrated in FIG. 18, to produce alignedtransverse sections. According to an embodiment, the aligned images 190are sequential ordered from the first end 102 to the second end 103, orvice versa. Each representation of a transverse section 110 in each ofthe images is translated so as to position each center point 185 on thesimulated axis 186, as illustrated in FIG. 11. FIG. 10, for examples,illustrates the an uncorrected axis 64 that passes through the centerpoints 63 of representations of uncorrected images 60, and a simulatedaxis 186 according an embodiment of the invention.

After the images are aligned, embodiments of the invention can furtherinclude cropping in step 639 of FIG. 39, a portion of each of theplurality of aligned transverse sections 191 for core surface artifactremoval to produce cropped aligned transverse sections 191. FIG. 20illustrates a cropped aligned image 190, and FIG. 19 illustrates aplurality of cropped aligned transverse sections 191 according to anembodiment of the invention. Embodiments of the invention can alsoinclude an artifact removal process that includes the steps of, forexample, determining in step 640, an imaginary circle 211 having asmaller radius than the approximated circle 180 to thereby identify anartifact removal circle, and discarding in step 641, portions of eachaligned transverse section that extends outwardly beyond the artifactremoval circle. After artifact removal, embodiments of the invention canfurther include generating in step 605, a three-dimensional simulatedmodel 300 of the core sample of the internal composition of thestructural characteristics of the core sample.

Embodiments of the present invention also include computer-implementedmethods, systems, and one or more non-transitory memories having one ormore computer programs for saw cut correction. As understood by thoseskilled in the art, a portion of the core sample is sometimes removed(e.g., a slab cut) with a cutting tool to facilitate removing the coresample from the borehole. As illustrated in FIG. 25, this causes thecore sample to have two pieces that are often put together duringimaging as illustrated in FIG. 22 for example. This is sometimes anundesirable processing artifact. Accordingly, embodiments of theinvention include, for example, computer-implemented methods, systems,and one or more non-transitory memories storing one or more computerprograms to adjust the images of the core sample to more accuratelyreflect the shape of the core sample before the saw cut line was made.In some embodiments of the invention, the saw cut correction 52 can beperformed after image registration 51 of the images, as indicated inFIG. 2, for example. In other embodiments, the saw cut correction 52 isperformed without image registration.

General aspects of the saw correction process, according an embodimentof the invention, can be described briefly with reference to FIG. 40.Saw cut correction embodiments can include, for example, the steps ofidentifying in step 650, a saw cut line of aligned representations,comparing in step 651, a number of non-zero pixels on a first side ofthe saw cut line to a number of non-zero pixels on a second side of thesaw cut line to thereby identify the smaller and larger portions of thecore sample. The smaller portion of the core sample being, for example,the portion of the representation associated with the smaller number ofnon-zero pixels relative to the saw cut line, and the larger portion ofthe core sample being, for example the portion of the representationassociated with the larger number of non-zero pixels relative to the sawcut line. Embodiments of the saw cut correction process can alsoinclude, for example, approximating in step 652, the slab cut boundaryof the aligned representations, and moving in step 653, the smallerportion of the representation to a point on the periphery of theapproximated circular boundary to thereby adjust the image for the slabcut. More particular aspects of the saw cut correction process,according to various embodiments, can be explained with reference toFIG. 41 for example.

To facility identifying the saw cut line, embodiments of the presentinvention can include superimposing at step 681 in FIG. 41, a pluralityof aligned transverse sectional images onto one another. Vugs, which aresmall cavities in the subsurface material, and the saw cut line 284 inthe images have similar characteristics (e.g., pixel values at or nearzero). Stacking the plurality of transverse sectional images 190enhances the characteristics of the saw cut line 284 and attenuates thesignature of vugs. Unlike the saw cut line, vugs, for example, areunlikely to be at the same or close to the same x and y locations imageafter image.

FIG. 28 illustrates, for example, one of the plurality of stackedaligned transverse sectional images 190 according to an embodiment ofthe invention. After the images 190 are stacked, the background 152 ofthe stacked aligned images can be discarded at step 681 of FIG. 41 tofurther enhance the characteristics of the saw cut line 284 such asillustrated in FIG. 30, for example. After the images 190 are stackedand the background is discarded or cropped, embodiments of the inventioncan further include identifying at step 682 of FIG. 41, two or morepixels in the one or more stacked representations 190 that have a valueof substantially zero and determining at step 683 an imaginary best-fitline 284 for the identified zero-value pixels 283 to thereby identifythe saw cut line 284. FIG. 31, for example, illustrates the saw cut line284 according to an embodiment of the invention.

As discussed above, when the core sample is removed from the borehole, asaw cut line 284 is sometimes made and the core sample is often cut intotwo portion portions. In addition to identifying the saw cut line 284,embodiments of the invention can also include, for example, identifyingthe smaller and larger portions of the core sample relative to the sawcut line 284. To do this, embodiments include, for example, comparing atstep 685 in FIG. 44, the number of non-zero pixels on a first side ofthe saw cut line 284 to the number of non-zero pixels on a second sideof the saw cut line 284. Dark pixels such as dark blue or black havevalues that are at or near zero. Accordingly, identifying the non-zeropixels (or a pixels equal to or greater than a predetermined number)according to embodiments of the invention will identify the pixelsassociated with the representation of the core sample. The section ofthe representation with the smallest number of pixels is the smallerportion 286 of the core sample, as illustrated in FIG. 29 for example,and the section with the largest number of pixels is the larger portion299 of the core sample.

Embodiments of the present invention can further include identifying instep 686, a point positioned on the periphery of the smaller portion ofthe representation to thereby identify a standalone point 287. Thestandalone point 287 can be used to adjust the image for the width ofthe piece of the core sample that was removed from the core sample. Thisis the estimated saw cut width as will be appreciated by those skilledin the art. According to some embodiments, the standalone point 287 canbe identified by locating the first non-zero pixel on the smallerportion 286 that is perpendicular to the perpendicular bisector 220 ofthe periphery of the image. In FIG. 32, for example, the top side of theimage is closest to the smaller potion 286 of the representation. Inthis example embodiment, the standalone point 287 can be determined bylocating the one or more first non-zero pixels when moving from aninitial position of the top side of the image towards the center of therepresentation (e.g., moving in a direction parallel to the saw cut line284). As will be understood by those skilled in the art, with thediscarded background, the area between the periphery of the image andthe boundary of the representation will be substantially devoid of colorpixels, and the representation of the core sample will include colorpixels. Accordingly, identifying one or more first non-zero pixels onthe smaller portion 286 of the representation will identify one or morepixels on an upper end of the representation of the core sample.

Embodiments of the saw cut correction can also include approximating instep 687 of FIG. 41, the substantially circular location of the boundaryof the stacked representation 190 with a slab cut to thereby identifythe approximate slab cut boundary 285. More specific aspects ofapproximating the slab cut boundary, according to an embodiment of theinvention, are illustrated in the flow chart in FIG. 42 for example. Toapproximate the slab cut boundary 285, embodiments of the inventioninclude computer-implemented methods, systems, and computer programsimplemented by one or more computer processors to automaticallydetermine in step 660 of FIG. 42, the perpendicular bisectors 220 oneach side of the image 190, and selecting in step 661, four or morepoints 205 on the larger portion of the representation 299 thatintersect with the perpendicular bisectors 220. FIG. 15, for example,illustrates four points 205 on the larger portion 299 that areperpendicular to the points 220 on the periphery of the image 190.

The perpendicular bisectors 220 of the image, for example, can bedetermined by calculating the number of pixels per direction anddividing this number by half for each side of the image. Points 205 onthe representation 151 are automatically determined, according tovarious embodiments, by locating, for example, one or more firstnon-zero pixels when moving from an initial position of a side of theimage towards the center of the larger portion 299 of therepresentation. Pixels of the representation 151 are in color accordingto an embodiment of the invention. Accordingly, identifying one or morefirst non-zero pixels (e.g., color pixels) on the larger portion 299 ofthe representation will identify one or more points 205 on the boundary153 of the larger portion 299 of the representation 151 of the coresample according to an embodiment of the invention. In some embodiments,four or more points 205 on the larger portion 299 of the representation151 are selected. In other embodiments, less than four points 205 on therepresentation 151 are selected. According to an exemplary embodiment,the selected points 205 on the representation 151 are perpendicular tothe perpendicular bisectors 220 of the image 150 as illustrated in FIG.25 for example. According to certain embodiments, the selected points205 on the larger portion 299 of the representation are notperpendicular to the perpendicular bisector 220 of the image 150 but areidentified as being one or more first non-zero pixel and therefore onthe boundary 153 of the representation 151.

After the points 205 on the larger portion 299 of the representation areselected, embodiments of the invention can further include determiningin step 662 of FIG. 42, imaginary circles 211 for each of the four ormore points 205 on the larger portion 299 of the representation. Aspectsof determining the imaginary circles 211 for the slab cut boundary,according to an embodiment of the invention, can further be describedwith reference to FIGS. 43 and 47. Determining or forming an imaginarycircle 211 for each of the four points 205 on the larger portion 299 ofthe representation can include, for example, selecting in step 670 ofFIG. 43, three of the four points to form an imaginary triangle 800, asillustrated in FIG. 47. An imaginary triangle 800 is formed for eachmathematical combination of three of the four selected points 205.Embodiments can further include, for example, determining in step 671,the circumcenter 801 of the imaginary triangle 800, and determining instep 660 an imaginary circle 211 for each of the four points 205, wherethe center of each of the imaginary circles is the circumcenter 801 ofthe imaginary triangle 800, as illustrated in FIG. 47. According toother embodiments, more or less points 205 on the representations areselected to determine the imaginary circles 211. According to certainembodiments, to determine the imaginary circles 211, the mathematicalcombinations of a subset of the selected points 205 on therepresentation are selected such that the peripheries of the imaginarycircle 211 interconnects the subset of the selected points.

FIG. 15, for example, illustrates four imaginary circles 211, one foreach of the four points 205 on the larger portion 299 of therepresentation. In this example embodiment, each circle 211interconnects three of the four points 205 on the larger portion 299 ofthe representation. After the imaginary circles 211 are determined foreach of the points 205 on the boundary 153 of the larger portion 299 ofthe representation, embodiments of the invention can further includecalculating in step 662 of FIG. 42, the radii of the imaginary circles211 (see e.g., the lines connected to the center 210 of each imaginarycircle 211 in FIG. 25) and calculating in step 663, the differencebetween each imaginary circle radius and a predetermined radius of thecore sample. Embodiments can further include, for example, selecting instep 664, the circle 212 with the smallest difference between its radiusand the radius of the core sample as the approximated slab cut boundary285 of the representations. In the example embodiment illustrated inFIG. 25, the circle 212 is the approximated slab cut boundary 285. Incertain embodiments, the slab cut boundary 285 is approximated usingpoints only on the smaller portion 286 of the representation, and inother embodiments, the boundary is approximated using points on both thesmaller 286 and larger 299 portions of the representation. FIG. 32, forexample, illustrates the approximated slab cut boundary 285 and thestandalone point 287 according to an embodiment of the invention.

The distance 287 between the standalone point 287 on the smaller portion286 and the approximated slab cut boundary 285, as illustrated in FIGS.32 and 33, is the distance 287 the smaller portion 286 of therepresentation is moved to account for the portion of the core samplethat was removed from the core sample according to an embodiment of theinvention. To move the smaller portion 287, embodiments of the inventioninclude, for example, determining in step 687 of FIG. 41, an imaginaryline 288 that is perpendicular to the saw cut line 284 and that extendsthrough the standalone point 287 to thereby identify a reference line288, as illustrated in FIGS. 29 and 33. The smaller portion 286 is thenmoved in step 689, parallel to the reference line 288 such that thestandalone point 287 is on the peripheries of the approximated slab cutboundary 285. The adjusted images more accurately reflect the originalshape of the core sample because they have been adjusted to reflect theapproximate portion of the core sample that was removed when the samplewas cut from the borehole. FIG. 22, for example, illustrates an image ofa representation of the core sample before the image is adjusted toaccount for the slab cut. FIG. 23, for example, illustrates the imageafter being adjusted to account for the slab cut according to anembodiment of the invention. FIG. 24 illustrate the estimated width ofthe slab cut 265 according to an embodiment of the invention.

As indicated in FIG. 2, after saw-cut correction 52, a series of imagescan undergo artifact removal 53. Artifact removal 53 can includeeliminating part of a representation 151 of a transverse section 110 inan image 150 to minimize the effects of any noise in the image 150.Noise can result from a variety of sources, including the process ofcoring and the process of acquiring images of transverse sections of acore sample 100. Artifact removal 53 can include cropping a portion ofthe representation 151 of a transverse section 110 such that therepresentation 151 becomes substantially circular in shape, asillustrated in FIGS. 19 and 20, for example.

After artifact removal 53, the series of images can undergo a beamhardening correction 54. Beam hardening can occur during CT scan (CTS)imaging and causes measured CT values to be higher for measurementstaken towards the edge of a core sample 100. Beam hardening results fromunequal absorption at different energies in a polychromatic x-ray beam:the energy distribution changes as the x-rays 32 permeate the coresample 100 such that the material of the core sample 100 filters photonswith lower energies. Consequently, measurements can include lowerattenuations from the center of a core sample 100 and higherattenuations from the edges of the core sample 100. CTS images cantherefore benefit from a correction for this effect. A polynomialregression can include a distance from the imaginary axis 104 of thecore sample 100 as an independent variable and computerized tomographyvalue measurements as the dependent variable. After beam hardeningcorrection 54, the series of images can be used to model the core sample100 that was imaged and ultimately to model a borehole based on the coresample 100 using multi-point statistics techniques with a core samplemodel 300 as a training image.

As discussed above, embodiments of the invention also include systems toprocess two-dimensional images of two-dimensional transverse sections110 of a real, substantially cylindrical core sample 100 of subsurfacematerial so as to be able to simulate a three-dimensional model 300 ofthe core sample 100. A system, for example, as shown in FIG. 26, caninclude one or more computers having one or more processors 11, an inputand output unit 12 in communication with the one or more processors 11,one or more displays 13 in communication with the one or more processors11, and non-transitory memory 14 in communication with the one or moreprocessors 11. The non-transitory memory 14 can includecomputer-readable instructions such as a computer program 70 that whenexecuted causes the system to perform a series of steps to manipulateimages of two-dimensional transverse sections 110 of a core sample 100so as to simulate a model 300 of the core sample 100. As illustrated inFIG. 34, for example, the computer program 70 can include theinstructions such as, image registering in step 71, a plurality oftwo-dimensional images of transverse sections of a core sample toproduce aligned transverse sections. Computer program embodiments canfurther includes the instructions such as, performing in step 72, a sawcut correction on aligned transverse section images, and generating instep 73, a three-dimensional simulated model of the core sample usingone or more of the saw cut corrected images. The computer programs caninclude, for examples, one or more computer modules adapted to performinstructions according to embodiments of the invention. The computerscan be further adapted to communicate over a communication network.According to an embodiment of the invention, the system includes one ormore first computers adapted to work in conjunction with the imagecapturing devices and connected to a communication network tocommunicate the captured images to one or more second computers adaptedto process the images to develop, for example, models of the coresample.

As will be understood with reference to the paragraphs above and thereferenced drawings, various embodiments of computer-implemented methodsare provided herein, some of which can be performed by variousembodiments of apparatuses and systems described herein and some ofwhich can be performed according to instructions stored innon-transitory computer-readable storage media described herein. Still,some embodiments of computer-implemented methods provided herein can beperformed by other apparatuses or systems and can be performed accordingto instructions stored in non-transitory storage mediums other than thatdescribed herein, as will become apparent to those having skill in theart with reference to the embodiments described herein. Any reference tosystems and computer-readable storage media with respect to thefollowing computer-implemented methods is provided for explanatorypurposes, and is not intended to limit any of such systems and any ofsuch computer-readable storage media with regard to embodiments ofcomputer-implemented methods described. Likewise, any reference to thefollowing computer-implemented methods with respect to systems andcomputer-readable storage media is provided for explanatory purposes,and is not intended to limit any of such computer-implemented methodsdescribed.

As used throughout this application, the words “may” or “can” are usedin a permissive sense (i.e., meaning having the potential to), ratherthan the mandatory sense (i.e., meaning must). The words “include”,“including”, and “includes” mean including, but not limited to. As usedthroughout this application, the singular forms of articles, such as“a”, “an” and “the,” include plural referents unless the content clearlyindicates otherwise. Unless specifically stated otherwise, as apparentfrom the discussion, it is appreciated that throughout thisspecification discussions utilizing terms such as “processing”,“computing”, “calculating”, “determining” or the like refer to actionsor processes of a specific apparatus, such as a special purpose computeror a similar special purpose electronic processing/computing device. Inthe context of this specification, a special purpose computer or asimilar special purpose electronic processing/computing device iscapable of manipulating or transforming signals, typically representedas physical electronic, optical, or magnetic quantities within memories,registers, or other information storage devices, transmission devices,or display devices of the special purpose computer or similar specialpurpose electronic processing/computing device.

In the drawings and specification, there have been disclosed embodimentsof the embodiments of methods, systems, and non-transitorycomputer-readable medium having computer program stored therein of thepresent invention, and although specific terms are employed, the termsare used in a descriptive sense only and not for purposes of limitation.The embodiments of methods, systems, and non-transitorycomputer-readable medium having computer program stored therein of thepresent invention have been described in considerable detail withspecific reference to these illustrated embodiments. It will beapparent, however, that various modifications and changes can be madewithin the spirit and scope of the embodiments of methods, systems, andnon-transitory computer-readable medium having computer program storedtherein of the present invention as described in the foregoingspecification, and such modifications and changes are to be consideredequivalents and part of this disclosure.

That claimed is:
 1. A computer-implemented method to processtwo-dimensional images of a core sample, the method comprising:approximating, using one or more computer processors, a circularboundary for each of a plurality of polygon shaped images of asubstantially cylindrical core sample, each image having arepresentation of a different transverse section of the core sample anda background that substantially surrounds the representation; selecting,using one or more computer processors, a center point of each of theapproximated circular boundaries of the images to define a referencepoint; determining, using one or more computer processors, an imaginaryline passing through the reference point of a first end of therepresentation of one of the plurality of transverse sections andextending substantially perpendicular to the plane of the representationof the first end to thereby define a simulated axis; and aligning, usingone or more computer processors, each of the representations oftransverse sections along the simulated axis, each reference point beingpositioned on the simulation axis.
 2. A computer-implemented method asdefined in claim 1, wherein approximating the circular boundarycomprises the steps of: determining a perpendicular bisector of eachside of the images; selecting four or more points on the representationthat intersects with the perpendicular bisectors; for each of the fouror more points, selecting at least three out of the four or more pointsto form an imaginary triangle; determining a circumcenter of each of theimaginary triangles; determine a radius of a plurality of imaginarycircles, the center of each of the imaginary circles being one ofcircumcenters of the imaginary triangles; comparing each radius of theplurality of imaginary circles to a predetermined radius of the coresample; and selecting the circle having the smallest difference betweenits radius and the predetermined radius of the core sample to define theapproximated circular boundary.
 3. A computer-implemented method asdefined in claim 1, wherein the approximating the circular boundarycomprises the steps of: determining four or more points on therepresentation; determining an imaginary circle for each of the four ormore points, each imaginary circle interconnecting a subset of at leastthree of the four or more points on the representation; and selectingthe imaginary circle having the smallest difference between its radiusand a predetermined radius of the core sample to define the approximatedcircular boundary.
 4. A computer-implemented method as defined in claim1, wherein the method further comprises: generating a three-dimensionalsimulated model of the internal composition of the structuralcharacteristics of the core sample on a display using the alignedrepresentation of the transverse sections of the core sample.
 5. Acomputer-implemented method as defined in claim 4, wherein the methodfurther comprises: generating a three-dimensional simulated model of theinternal composition of the structural characteristics of a borehole onthe display using the aligned representation of the transverse sectionsof the core sample.
 6. A computer-implemented method of claim 1, whereinthe method further comprises, before approximating the circularboundary, capturing a plurality of two-dimensional images of a pluralityof transverse sections of the core sample using a core sample imagingdevice.
 7. A computer-implemented method of claim 1, wherein the methodfurther comprises, cropping a portion of each of the plurality ofaligned transverse sections to remove core surface artifact to therebyform simulated peripheries to be substantially similar in size and todefine a plurality of cropped aligned transverse sections, the croppedaligned transverse sections to include the aligned representations ofthe transverse sections and to exclude cropped portions; and generatinga three-dimensional simulated model of the internal composition of thestructural characteristics of the core sample on a display using thealigned representation of the transverse sections of the core sample. 8.A system to process two-dimensional images of the internal compositionof the structural characteristics of a real, three-dimensional,substantially cylindrical core sample of subsurface material to simulatea three-dimensional model, the system comprising: one or moreprocessors; an input and output unit in communication with the one ormore processors; one or more displays in communication with the one ormore processors; and one or more non-transitory memories incommunication with the one or more processors, the one or more memorieshaving one or more computer programs with computer-readable instructionsstored therein that when executed cause the system to perform the stepsof: approximating, using the one or more computer processors, a circularboundary for each of a plurality of polygon shaped images of asubstantially cylindrical core sample, each image having arepresentation of a different transverse section of the core sample anda background that substantially surrounds the representation, theapproximating being responsive to receiving the plurality of imagesthrough the input and output unit; selecting, using one or more computerprocessors, a center point of each of the approximated circularboundaries of the images to define a reference point; determining, usingthe one or more computer processors, an imaginary line passing throughthe reference point of a first end of the representation of one of theplurality of transverse sections and extending substantiallyperpendicular to the plan of the representation of the first end tothereby define a simulated axis; and aligning, using the one or morecomputer processors, each of the representations of transverse sectionsalong the simulated axis, each reference point being positioned on thesimulation axis.
 9. A system as defined in claim 8, wherein the computercomputer-readable instructions further cause the system to approximatethe circular boundary by perform the steps of: determining aperpendicular bisector of each side of the images; selecting four ormore points on the representation that intersects with the perpendicularbisectors; for each of the four or more points, selecting at least threeout of the four or more points to form an imaginary triangle;determining a circumcenter of each of the imaginary triangles; determinea radius of a plurality of imaginary circles, the center of each of theimaginary circles being one of circumcenters of the imaginary triangles;comparing each radius of the plurality of imaginary circles to apredetermined radius of the core sample; and selecting the circle havingthe smallest difference between its radius and the predetermined radiusof the core sample to define the approximated circular boundary.
 10. Asystem as defined in claim 8, the system further comprising: an imagecapturing device adapted to capture a plurality of images of the coresample; and wherein the input output unit is adapted to receive theplurality of images from the image capturing device.
 11. A system asdefined in claim 8, wherein the computer computer-readable instructionsfurther cause the system to approximate the circular boundary by performthe steps of: determining four or more points on the representation;determining an imaginary circle for each of the four or more points,each imaginary circle interconnecting a subset of at least three of thefour or more points on the representation; and selecting the imaginarycircle having the smallest difference between its radius and apredetermined radius of the core sample to define the approximatedcircular boundary.
 12. A system as defined in claim 8, wherein thecomputer computer-readable instructions further cause the system toperform the steps of: generating a three-dimensional simulated model ofthe internal composition of the structural characteristics of the coresample on a display using the aligned representation of the transversesections of the core sample.
 13. A system as defined in claim 12,wherein the computer computer-readable instructions further cause thesystem to perform the steps of: generating a three-dimensional simulatedmodel of the internal composition of the structural characteristics of aborehole on the display using the aligned representation of thetransverse sections of the core sample.
 14. A system as defined in claim8, wherein the computer computer-readable instructions further cause thesystem to perform the steps of: cropping a portion of each of theplurality of aligned transverse sections to remove core surface artifactto thereby form simulated peripheries to be substantially similar insize and to define a plurality of cropped aligned transverse sections,the cropped aligned transverse sections to include the alignedrepresentations of the transverse sections and to exclude croppedportions; and generating a three-dimensional simulated model of theinternal composition of the structural characteristics of the coresample on a display using the aligned representation of the transversesections of the core sample.
 15. A system as defined in claim 8, whereinthe computer computer-readable instructions further cause the system toperform the step of, before approximating the circular boundary,capturing a plurality of two-dimensional images of a plurality oftransverse sections of the core sample using a core sample imagingdevice.
 16. Non-transitory memory having one or more computer programsstored then, the computer programs having computer-readable instructionsthat when executed cause one or more computer processors to perform thesteps of: approximating, using the one or more computer processors, acircular boundary for each of a plurality of polygon shaped images of asubstantially cylindrical core sample, each image having arepresentation of a different transverse section of the core sample anda background that substantially surrounds the representation, theapproximating being responsive to receiving the plurality of imagesthrough the input and output unit; selecting, using one or more computerprocessors, a center point of each of the approximated circularboundaries of the images to define a reference point; determining, usingthe one or more computer processors, an imaginary line passing throughthe reference point of a first end of the representation of one of theplurality of transverse sections and extending substantiallyperpendicular to the plan of the representation of the first end tothereby define a simulated axis; and aligning, using the one or morecomputer processors, each of the representations of transverse sectionsalong the simulated axis, each reference point being positioned on thesimulation axis.
 17. Non-transitory memory as defined in claim 16,wherein the computer computer-readable instructions further cause theone or more computer processors to approximate the circular boundary byperform the steps of: determining a perpendicular bisector of each sideof the images; selecting four or more points on the representation thatintersects with the perpendicular bisectors; for each of the four ormore points, selecting at least three out of the four or more points toform an imaginary triangle; determining a circumcenter of each of theimaginary triangles; determine a radius of a plurality of imaginarycircles, the center of each of the imaginary circles being one ofcircumcenters of the imaginary triangles; comparing each radius of theplurality of imaginary circles to a predetermined radius of the coresample; and selecting the circle having the smallest difference betweenits radius and the predetermined radius of the core sample to define theapproximated circular boundary.
 18. Non-transitory memory as defined inclaim 16, wherein the computer-readable instructions further cause theone or more computer processors to perform the steps of: generating athree-dimensional simulated model of the internal composition of thestructural characteristics of the core sample on a display using thealigned representation of the transverse sections of the core sample.19. Non-transitory memory as defined in claim 16, wherein thecomputer-readable instructions further cause the one or more computerprocessors to perform the steps of: cropping a portion of each of theplurality of aligned transverse sections to remove core surface artifactto thereby form simulated peripheries to be substantially similar insize and to define a plurality of cropped aligned transverse sections,the cropped aligned transverse sections to include the alignedrepresentations of the transverse sections and to exclude croppedportions; and generating a three-dimensional simulated model of theinternal composition of the structural characteristics of the coresample on a display using the aligned representation of the transversesections of the core sample.
 20. Non-transitory memory as defined inclaim 16, wherein the computer-readable instructions further cause theone or more computer processors to perform the steps of: generating athree-dimensional simulated model of the internal composition of thestructural characteristics of a borehole on a display using the alignedrepresentation of the transverse sections of the core sample.